Please help. I need help with a couple of questions. I will give medal and fan.

- anonymous

Please help. I need help with a couple of questions. I will give medal and fan.

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- schrodinger

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- anonymous

A toy rocket was launched from the ground. The function f(x) = -16x^2 + 192x shows the height of the rocket f(x), in feet, from the ground at time x seconds.
What is the axis of symmetry of the graph of f(x), and what does it represent?
x = 12; it takes 12 seconds to reach the maximum height and 12 seconds to fall back to the ground
x = 12; it takes 12 seconds to reach the maximum height and 24 seconds to fall back to the ground
x = 6; it takes 6 seconds to reach the maximum height and 6 seconds to fall back to the ground
x = 6; it takes 6 seconds to reach the maximum height and 3 seconds to fall back to the ground

- anonymous

I think its either C or D

- anonymous

i think it is not a 100% sure though

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- anonymous

can you help me with a couple more?

- anonymous

yeah i will try

- anonymous

Functions f(x) and g(x) are shown below:
f(x) = x2
g(x) = x2 + 10x + 25
In which direction and by how many units should f(x) be shifted to obtain g(x)?
Right by 5 units
Left by 5 units
Right by 10 units
Left by 10 units

- Vocaloid

hint: (x^2 + 10x + 25) = (x+5)^2

- anonymous

so would it be D?

- Vocaloid

nope, please look carefully at what I wrote
(x+k)^2 moves the graph x^2 to the left k units

- anonymous

OK, B?

- Vocaloid

yes, B is the answer, but do you understand how to get (x+5)^2?

- anonymous

can you explain it a little, I sort of forgot.

- Vocaloid

have you seen this formula?
(a+b)^2 = a^2 + 2ab + b^2?

- anonymous

yes

- Vocaloid

great! in the equation x^2 + 10x + 25, do you see how x = a and b = 5? when you plug in x for a and b for 5, do you see how x^2 + 10x + 25 = (x+5)^2?
this is called "factoring", basically you want to find a and b so you can simplify x^2 + 10x + 25 into (x+5)^2

- anonymous

oh, I remember thanks!

- anonymous

do you mind helping me with a couple more?

- Vocaloid

sure, I guess

- anonymous

The steps to derive the quadratic formula are shown below:
Which of the following statements best describes the first incorrect step?
In Step 4, square of quantity of b over 2 times a instead of b over 2 times a was added on both sides.
In Step 5, x plus b over 2 times a, all squared was written instead of x plus b over 4a, all square.
In Step 6, c over a was written instead of -c over a inside the root.
In Step 7, square of quantity of b over 2 times a was written instead of b over 2 times a inside the root.

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- Vocaloid

http://www.purplemath.com/modules/sqrquad2.htm

##### 1 Attachment

- Vocaloid

NOTE: I got this from a website, I didn't write this out myself, but these are the steps to derive the quadratic equation

- anonymous

David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?

- anonymous

for this one I know you plug in the 35 for v but what do you plug in for s?

- Vocaloid

v = initial velocity = 35, s = initial height = 0

- Vocaloid

an object on the ground has a height of 0

- Vocaloid

initial height = 0, because the ball is on the ground

- anonymous

ok I can do this one by myself

- Vocaloid

k cool

- anonymous

can you help me with 3 more?

- Vocaloid

ok

- anonymous

Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.
What does the average rate of change of f(x) from x = 4 to x = 6 represent?
The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds.
The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds.
The water travels an average distance of 5 feet from 4 seconds to 6 seconds.
The water travels an average distance of 3 feet from 4 seconds to 6 seconds.

- anonymous

If 5p = -100 + 3Q2, which of the following could Q possibly be?
Q = square root of 5p-100/ 3
Q = square root of 5p+100/3
Q = square root of -5p+100/ 3
Q = square root of -5p-100/ 3

- Vocaloid

this one is a bit tough to explain but I'll try
average rate of change = speed = distance/time
the average rate of change between x = 6 seconds and x = 4 seconds =
distance travelled between 4 to 6 seconds/(6-4 seconds)
= [f(6)-f(4)]/(6-4)

- Vocaloid

and for the second one:
5p = -100 + 3Q^2
all you're doing is solving for Q in terms of p
add 100 to each side
divide each side by 3
take the square root of each side to find Q

- anonymous

35p=q^2
I got 5.9160797830996160425673282915616 when I did the square root of 35

- Vocaloid

??? I think you're confused, can I try outlining it step by step?

- anonymous

sorry I got confused I understand now.

- Vocaloid

|dw:1432846015012:dw|

- anonymous

the answer I got is B

- Vocaloid

yup! good job

- anonymous

|dw:1432846126778:dw|

- anonymous

I have one more. Do you think you can help me?

- anonymous

What is the domain of the following parabola?
x ≥ 2
x ≤ -1
y ≤ 3
All real numbers

##### 1 Attachment

- Vocaloid

are there any x values that don't have y values?

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